This article aims to present a comprehensive review of the recent efforts and advances in applying machine learning (ML) techniques in the area of diagnostics and prognostics of rolling element bearings (REBs). The main goal of this study is to review, recognize and evaluate the performance of various ML techniques and compare them on criteria such as reliability, accuracy, robustness to noise, data volume requirements and implementation aspects. The merits and demerits of the reviewed ML techniques have been comprehensively analyzed and discussed. A comparative benchmarking of the performance of the reviewed ML algorithms is provided both from the viewpoint of theoretical aspects and industrial applicability. Finally, the potential challenges that come along with the implementation of ML technology are discussed in detail that will likely play a major role in the prognostics and health management of REBs. It is expected that this review will serve as a reference point for researchers to explore the opportunities for further improvement in the field of ML-based fault diagnosis and prognosis of REBs.